Prove that the logarithmic function is strictly increasing on (0, ∞)

Solution:

Increasing functions are those functions that increase monotonically within a particular domain,

and decreasing functions are those which decrease monotonically within a particular domain.

Logs (or) logarithms are nothing but another way of expressing exponents.

Understanding logs is not so difficult.

To understand logs, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation

The given function is

f (x) = log x

Therefore,

f'(x) = 1/x

For, x > 0,

f' (x) = 1/x > 0

Thus,

the logarithmic function is strictly increasing in the interval (0, ∞)

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.2 Question 10

Prove that the logarithmic function is strictly increasing on (0, ∞).

Summary:

Hence we have concluded that the logarithmic function is strictly increasing on (0, ∞)